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FIGURE 36.2 Optimum reliability of a structure based on total life cycle cost.

These two simple examples illustrate the difference between a traditional design approach, which relies only on the initial cost of the structure, and the life cycle cost approach, which includes all costs over the useful life of the structure. These total life cycle costs are the sum of the initial cost, maintenance costs, inspection and repair costs, and cost of failure. The failure cost typically comprises those costs associated with structural failure multiplied by their probability of occurrence. Incorporating the failure cost requires a probabilistic assessment of the structure, which by necessity requires a reliability-based approach to the problem. Once the costs have been computed and included, an optimum solution, as shown in Figure 36.2, produces the lowest total life cycle cost.

While the life cycle cost is a better measure on which to make a decision, the approach is more complex and introduces many additional issues and considerations over the traditional approach. The discount rate is only one consideration. Others include the following: what costs are included in the failure cost, what is the effect of maintenance on the reliability of a structure, how is a structure expected to deteriorate over time, how far can a structure be allowed to deteriorate before public safety requires a repair, how often should a structure be inspected and how reliable is the information provided by each inspection? The answers to these questions are the subject of frequent debate and the focus of considerable research. The approaches are still being developed. This chapter will address many of these issues, show some relevant examples, and provide some initial solutions to this evolving field.

36.2 Safety and Risk Assessment

Society expects its infrastructure to be safe and depends on its engineers to make it so. The American Society of Civil Engineers (ASCE) canon of ethics requires that the safety of the public is paramount. Sadly, there is no absolute guarantee of safety, and if there was, it would be prohibitively expensive. Risk is usually defined as the product of the failure probability and the consequences (i.e., measured in monetary terms) of failure. The responsibility of civil engineers is to find an acceptable level of risk that society can tolerate and then design and maintain structures to ensure that risk is not exceeded. Engineers are expected to do this within a reasonable cost, which becomes both a balancing act and an optimization problem. Even a deterministic approach to structural analysis attempts to define safety, usually in the form of a factor of safety. Reliability methods offer a more detailed accounting of risk that involves quantifying the uncertainty associated with every variable, the correlation between the variables, the system relationship between structural components, and the consequences of failure. Reliability methods are complex and require significant input data to execute. An elementary example is illustrated as follows.

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